Multiple mean motion resonances in the HR 8799 planetary system

Abstract

HR 8799 is a nearby star hosting at least four ∼ 10 m Jup planets in wide orbits up to ∼ 70 au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ∼ 10 au, and exterior to ∼ 100 au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ∼ 25 • to the sky plane. This best-fit orbital configuration matches astrometry, debris disk models, and mass estimates from cooling models. The multiple MMR is stable for the age of the star ∼ 160 Myr, for at least 1 Gyr unless significant perturbations to the N-body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ∼ 9.7 au, or ∼ 7.5 au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.

The LEECH Exoplanet Imaging Survey. Further constraints on the planet architecture of the HR 8799 system

“…We also indicate in Fig. 3 the ephemeris predicted by Goździewski & Migaszewski (2014) for a four-planet system (see their Appendix B.1) at the epoch of the observations presented in this paper. The presence of a putative fifth planet inside the known planets does not affect the ephemeris of the known planets significantly.…”

“…For resonance 3e:1f, Goździewski & Migaszewski (2014) predict a separation and a mass range for "HR 8799 f" of ∼7.4 AU and about two to eight Jupiter masses (M J ), while for resonance 2e:1f, they derive values of ∼9.7 AU and ∼1.5-5 M J . Given the contrast curve in the lefthand panel of Fig.…”

“…The planet masses and the detection limits are derived from two models: the "hotstart" model COND (Baraffe et al 2003) coupled with the atmosphere model BT-Settl (Allard et al 2012) and the "warmstart" evolutionary and atmosphere model of Spiegel & Burrows (2012) corresponding to an initial entropy of 9 k B /baryon and a cloudy atmosphere of one solar metallicity 4 . The value for the initial entropy is selected based on the work of Marleau & Cumming (2014), assuming an upper limit for the planet masses of 12 M J according to the dynamical analysis of Goździewski & Migaszewski (2014) 5 . The selected value for the initial entropy is thus the approximate minimum value allowed for the formation of the planets independently from the details of the formation scenario.…”

“…The range will be shifted towards higher masses when assuming older ages. However, constraints from the stellar properties (Marois et al 2008;Baines et al 2012), the mass of the disk (Su et al 2009), and models of dynamical stability of the four planets (Esposito et al 2013;Goździewski & Migaszewski 2014) suggest that the system is young. Other hints for small radii or low masses of the planets come from the fitting of their spectral energy distribution (e.g., Marois et al 2008;Bowler et al 2010;Currie et al 2011;Barman et al 2011;Madhusudhan et al 2011;Galicher et al 2011;Ingraham et al 2014), although there are uncertainties on the atmospheric composition and the physical processes governing their atmospheres assumed for the models (e.g., solar/non-solar metallicity, physics of the clouds, non-equilibrium chemistry).…”

“…Recently, Goździewski & Migaszewski (2014) have built a long-term stable model of the system, with all planets on quasi-circular coplanar orbits and likely involved in 8b:4c:2d:1e mean motion resonance. We first tested the predictions of Goździewski & Migaszewski (2014) with respect to the astrometric measurements presented in this paper. We gathered all the relative astrometric measurements available in the literature (Marois et al 2008(Marois et al , 2010bLafrenière et al 2009;Fukagawa et al 2009;Metchev et al 2009;Hinz et al 2010;Currie et al 2011Currie et al , 2012Currie et al , 2014Bergfors et al 2011;Galicher et al 2011;Soummer et al 2011;Esposito et al 2013;Pueyo et al 2015) and included the LEECH measurements (Table 2) to represent Fig.…”